It leaves the series without two of its big-name batsmen after India great Sachin Tendulkar was ruled out Monday with a toe problem.
The England and Wales Cricket Board says Morgan first hurt his shoulder during the Ashes tour in Australia at the start of the year before injuring it again in the Twenty20 win against India last week.
England's chief medical officer Nick Peirce says "this is a chronic injury and predominantly affects Eoin's diving and throwing." Renowned for his inventive shot-making skills, the Irish-born limited-overs specialist is a key member of England's middle order.